Wednesday, September 30, 2015

Recommended statistics book

Hopefully my silence here over the past two weeks can be interpreted as being due to a period of hard work interspersed with holidays in which I have done little. That description corresponds quite well to the truth.

Over the past few days, I've been working once again on the statistical analysis of the interim data collected during the pilot study of my doctorate. This follows an interchange with my mentor whom at first I thought was misunderstanding me; it turns out that I was misunderstanding him. I should try to remember that whenever he writes something which seems to be wrong, he is writing from a position of knowledge and so I should try and see from his point of view what is wrong.

It appears that I was labouring under a misunderstanding regarding some of the variables, and I've been working on redefining them. To recap, a variable can be one of four types: interval (eg age, IQ, years of employment), ordinal (data which can be ranked, but the gaps between each value are not constant), nominal (name only, eg religion, department) and dichotomous (two values only, eg gender).

Only data from interval variables can be aggregated; my mistake was trying to aggregate ordinal data. Having improved my understanding, I can now see how the misunderstanding arose: ordinal data can participate in multiple regression analysis (where each option is assigned a dummy value), but one can't aggregate those dummy values from more than one question.

So whereas before I had one variable called 'Training', composed of the aggregate value of three questions, I now have three variables entitled 'frequency of training', 'type of training' and 'quality of training'. These variables are compared to the dependent variable (use of spreadsheets with Priority data) by means of ANOVA and the F-test.

I can recommend the book "Statistics: a tool for social research" by Joseph F. Hailey as being both a good introduction and also a companion for the calculations required in my research. Unlike other books which I have read on the subject, Hailey begins with the four types of variables and notes which mathematical operations can be carried out of which type of variable. Of course, he carries on to show which analytical tools can be used on which type of variable. 

Although I had read about ANOVA elsewhere, the material had not been presented in the way which allowed me to make the connection with my data. In fact, there is a detailed ANOVA calculation in the 'Introduction to Business Research 3' course, but again this was presented in a slightly different way. IBR3 makes no mention whatsoever of the four variable types, which I think is a shame. I shall point this out to my mentor.

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